1. Field of the Invention
The present invention relates to electrical and electronic circuits and systems. More specifically, the present invention relates to systems and methods for Q enhancement for passive inductive capacitive resonators in electrical and electronic circuits and systems.
2. Description of the Related Art
In reference to a resonant mechanical or electrical circuit or a capacitor, Q is a “quality factor.” In the case of a resonant system, Q is a measure of the sharpness of the resonant peak in the frequency response of the system and is inversely proportional to the damping in the system: Q=center frequency divided by Hz bandwidth. Equalizers that contain resonant circuits are rated by their Q-value: the higher the Q, the higher and more well defined the peak in the response. In filters, the ratio of a bandpass or band-reject filter's center frequency to its bandwidth defines Q. Thus, assuming a constant center frequency, Q is inversely proportional to bandwidth, i.e., a higher Q indicates a narrower bandwidth. (See http://www.dilettantesdictionary.com/pdf/q.pdf.)
Hence, for a variety of applications such as analog to digital conversion, wireless communication circuits, narrowband amplifiers, microwave circuits and the like, it is useful to provide a system or method for Q enhancement.
In analog signal processing and communication systems, Q enhancement circuits typically use negative resistor circuits to cancel out parasitic serial resistance associated with the inductors (L) in the passive inductor-capacitor (LC) resonators. When implemented in fully differential mode, these circuits are usually connected in parallel with the capacitors of the resonator and typically the capacitor is connected between two inductors. Generally, the negative resistor circuits fail to adequately cancel the parasitic resistance of the inductors. This non-ideal cancellation causes other second order effects and can cause the circuit to resonate at other frequencies.
In addition, the use of negative resistors requires voltage-to-current converters to generate negative currents for the cancellation. This makes the negative resistor circuit more susceptible to non-linear distortion and circuit delay and degrades the performance of the LC resonator.
Hence, a need remains in the art for a system or method for enhancing the Q of a circuit. Particularly, a need remains in the art for a system or method for enhancing the Q of LC resonators used in analog signal processing and communication systems to improve the linearity and resolution thereof.